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Calgary Teacher’s
Convention
February 16, 2012
Chosen as the
EXCLUSIVE publisher
for the new
Pre-Calculus Grade 11& 12
courses
Opening Doors!
http://www.mcgrawhill.ca/school/tr/7D052003
http://learning.arpdc.ab.ca/
• Unit 1: Transformations and Functions
– Chapter 1: Function Transformations
– Chapter 2: Radical Functions
– Chapter 3: Polynomial Functions
• Unit 2: Trigonometry
– Chapter 4: Trigonometry and the Unit Circle
– Chapter 5: Trigonometric Functions and Graphs
– Chapter 6: Trigonometric Identities
• Unit 3: Exponential and Logarithm Functions
– Chapter 7: Exponential Functions
– Chapter 8: Logarithmic Functions
• Unit 4: Equations and Functions
– Chapter 9: Rational Functions
– Chapter 10: Function Operations
– Chapter 11: Permutations, Combinations, and the Binomial Theorem
Table of Contents
• Unit
•
•
•
•
•
•
•
•
•
•
•
•
Unit Opener
Unit Project
Chapters (2 or 3 per unit)
Sections (3 to 5 per chapter)
Investigate
3-Part
Link the Ideas
Lesson
Check Your Understanding
Chapter Review
Practice Test
Unit Project Wrap-Up
Cumulative Review
Unit Test
Math 30-1 Possible Course Outline September 2012 – January 2013
Chapter
Number of Days
Tentative Exam Date
Function Transformations
8
September 13
Radical Functions
6
September 21
Polynomial Functions
8
October 3
Trig and the Unit Circle
8
October 16
Trig Functions and Graphs
8
October 26
Trig Identities
8
November 6
Exponential Functions
6
November 16
Log Functions
7
November 27
Rational Functions
6
December 5
Function Operations
6
December 13
Perms/Combs
6
December 21
Chapter 1 Transformations
1.1
R Kennedy
Pre-Calculus 12, McGraw-Hill Ryerson
8
What is a Function?
A variable y is said to be a function of a variable x if there is a
relation between x and y such that every value of x corresponds to
one and only one value of y.
The symbol ‘ f (x) ’ may be used to denote a function of x.
For example, 4x + 5 is the function of x. It can be
expressed as f(x) = 4x + 5.
The letter ‘f ’ in the symbol ‘f(x)’ can be replaced by other letters,
for example,
h( x)  x 2 , g ( x)  x 2 or F ( x)  x 2
Besides x, we can have functions of other variables, for
example,
3u 2  4u  5 is a function of u and we may write
f (u )  3u 2  4u  5.
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Functions
linear
quadratic
absolute value
square root
logarithmic
cubic
reciprocal
cube root
exponential
sine
cosine
Line Dance
Graphs of Functions
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1.1.2
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Graph Translations of the Form y – k = f(x)
Given the graph
of y = |x|, graph
the functions
y = |x| + 8 and
y = |x| – 8.
The transformed
graphs are congruent
to the graph of y = |x|.
Each point (x, y) on the
graph of y = |x| is
transformed to
become the point
(x, y + 8) on the graph
of y = |x| + 8.
Ex: (–4, 4)  (–4, 12)
y = |x|+ 8
(-4, 12)
(-4, 4)
y = |x| – 8
(-4, -4)
It becomes the point
(x, y – 8) on the graph
of y = |x| – 8.
Ex: (–4, 4)  (–4, -4)
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Graphing y = f(x) + k
Graph y = |x| + 8
x
y = |x| y = |x|+8
–8
8
16
–6
6
14
–4
4
12
–2
2
10
0
0
8
2
2
10
4
4
12
6
6
14
8
8
16
The graph of a function is translated vertically if a constant is either added
or subtracted from the original function. Each point (x, y) on the graph of
y = |x| is transformed to become the point (x, y + 8) on the graph of
y – 8 = |x|. Using mapping notation,
(x, y) → (x, y + 8).
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Graph Translations of the Form y = f(x – h)
Given the graph
of y = |x|, graph
the functions
y = |x + 7| and
y = |x – 8|.
The transformed
graphs are congruent
to the graph of y = |x|.
Each point (x, y) on the
graph of y = |x| is
transformed to
become the point
(x – 7, y) on the graph
of y = |x + 7|.
Ex: (–4, 4)  (–11, 4)
(-11, 4)
(-4, 4)
(4, 4)
y = |x - 8|
y = |x + 7|
It becomes the point
(x + 8, y) on the graph
of y = |x – 8|.
Ex: (–4, 4)  (4, 4)
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Horizontal and Vertical Translations
Sketch the graph of y = |x – 4|– 3.
• Apply the horizontal
translation of 4 units to
the right to obtain the
graph of y = |x – 4|.
y = |x – 4|
• Apply the vertical
translation of 3 units
down to y = |x – 4| to
obtain the graph
of y = |x – 4| – 3.
The point (0, 0) on the
function y = |x| is
transformed to become
the point (4, -3). In
general, the
transformation can be
described as
(x, y) → (x + 4, y – 3).
(0, 0)
y = |x – 4| – 3
(4, -3)
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Transformation of functions y – k = f(x – h)
• Given the function
defined by a table
x
–3
–2
–1
0
1
2
3
f(x)
7
4
9
3
12
5
6
• Determine the coordinates of the following transformations
f(x) + 3
(–3, 10) (–2, 7) (–1, 12) (0, 6) (1, 15) (2, 8) (3, 9)
f(x + 1)
(–4, 7)
f(x – 2) + 4
(–3, 4)
(–1, 11) (0, 8)
(–2, 9) (–1, 3) (–2, 12) (–3, 5) (–4, 6)
(1, 13)
(2, 7) (3, 16) (4, 9) (5, 10)
Each point (x, y) on the graph of y = f(x)is transformed to become the point
(x + h, y + k) on the graph of y – k = f(x – h).
Using mapping notation, (x, y) → (x + h, y + k).
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Transformation of functions y – k = f(x – h)
Possible Assignment
Essential: #1 – 3, 5, 6, 8, 10 – 12, C1, C2, C4
Typical: #5, 7 – 12, 13 or 14, C1, C2, C4
Enrichment #15 – 19, C2 – C4
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There is an Australian software company called Atlassian and they
do something once a quarter where they say to their software
developers: You can work on anything you want, any way you
want, with whomever you want, you just have to show the results
to the rest of the company at the end of 24 hours. They call these
things Fed-Ex Days, because they basically have to deliver
something overnight. That one day of intense autonomy has
produced a whole array of software fixes, a whole array of ideas
for new products, and a whole array of upgrades for existing
products
What might emerge if we let kid loose to
work on anything they want for a day with
the only proviso that their presentation the
next day explain:
why they had undertaken this work,
how it used or connected with math and
what they had done?